Systems and methods for sliding convolution interpolating filters

Abstract

Certain embodiments of the invention may include systems and methods for implementing a multirate digital interpolating filter. According to an example embodiment of the invention, the method includes sampling symbol data from one sample per symbol to N samples per symbol, wherein sampling includes: convolving the symbol data with a decimated finite impulse response (FIR) aperture impulse response coefficient set, convolving the symbol data with one or more shifted decimated FIR aperture impulse response coefficient sets, and summing the convolution results to produce interpolated bandlimited data.

The claimed invention is: 
     
       1. A method for implementing a multirate digital interpolating filter comprising:
 sampling, by a computer comprising one or more processors, symbol data from one sample per symbol to N samples per symbol, wherein sampling comprises: 
 convolving, by the computer, the symbol data with a decimated finite impulse response (FIR) aperture impulse response coefficient set; 
 convolving, by the computer, the symbol data with shifted decimated FIR aperture impulse response coefficient sets; and 
 summing, by the computer, the convolution results to produce interpolated bandlimited data. 
 
     
     
       2. The method of  claim 1 , wherein sampling the symbol data comprises one or more of upsampling or spectral shaping symbol data. 
     
     
       3. The method of  claim 1 , wherein convolving the symbol data with shifted decimated FIR aperture impulse response coefficient sets comprises convolving, by the computer, the symbol data with one-to-N-shifted decimated FIR aperture impulse response coefficient sets, wherein the one-to-N-shifted decimated FIR aperture impulse response coefficient sets are shifted by one-to-N samples with respect to the decimated FIR aperture impulse response coefficient set. 
     
     
       4. The method of  claim 1 , further comprising filtering, by the computer, the interpolated bandlimited data to remove spectral replicas. 
     
     
       5. The method of  claim 1 , wherein sampling the symbol data comprises sampling, by the computer, digital symbols, wherein the digital symbols comprise one or more of in-phase or quadrature-phase symbol data. 
     
     
       6. The method of  claim 1 , wherein convolving the symbol data with the decimated FIR aperture impulse response coefficient set comprises convolving, by the computer, the symbol data with a Nyquist filtering function. 
     
     
       7. The method of  claim 1 , wherein sampling symbol the data provides a sample per symbol rate of powers-of-two times three or powers-of-two. 
     
     
       8. A system for implementing a multirate digital interpolating filter comprising:
 at least one memory for storing FIR aperture impulse response coefficients; 
 at least one processor configured to access the at least one memory and further configured to upsample symbol data from one sample per symbol to N samples per symbol, wherein upsampling comprises:
 convolving the symbol data with a decimated FIR aperture impulse response coefficient set; 
 convolving the symbol data with one or more shifted decimated FIR aperture impulse response coefficient sets; and 
 summing the convolution results to produce interpolated bandlimited data; and 
 
 at least one modulator for upconverting at least a portion of the interpolated bandlimited data. 
 
     
     
       9. The system of  claim 8 , wherein the symbol data comprises one or more of in-phase or quadrature-phase symbol data. 
     
     
       10. The system of  claim 8 , wherein convolving the symbol data with shifted decimated FIR aperture impulse response coefficient sets comprises convolving the symbol data with one-to-N-shifted decimated FIR aperture impulse response coefficient sets, wherein the one-to-N-shifted decimated FIR aperture impulse response coefficient sets are shifted by one-to-N samples with respect to the decimated FIR aperture impulse response coefficient set. 
     
     
       11. The system of  claim 8 , further comprising at least one filter configured to remove spectral replicas from the interpolated bandlimited data. 
     
     
       12. The system of  claim 8 , wherein the symbol data comprises digital data. 
     
     
       13. The system of  claim 8 , wherein the FIR aperture impulse response coefficient set comprises a raised cosine FIR aperture impulse response or an impulse response modeled from Nyquist filtering functions. 
     
     
       14. The system of  claim 8 , wherein the at least one processor is further configured to upsample symbol data at a sample per symbol rate of powers-of-two times three or powers-of-two. 
     
     
       15. The system of  claim 8 , further comprising one or more digital-to-analog converters. 
     
     
       16. A filter for sampling digital data comprising:
 at least one memory for storing FIR aperture impulse response coefficients; 
 at least one processor configured to access the at least one memory and further configured to upsample symbol data from one sample per symbol to N samples per symbol, wherein upsampling comprises:
 convolving the symbol data with a decimated FIR aperture impulse response coefficient set; 
 convolving the symbol data with one or more shifted decimated FIR aperture impulse response coefficient sets; and 
 summing the convolution results to produce interpolated bandlimited data. 
 
 
     
     
       17. The filter of  claim 16 , wherein the symbol data comprises one or more of in-phase or quadrature-phase symbol data. 
     
     
       18. The filter of  claim 16 , wherein convolving the symbol data with shifted decimated FIR aperture impulse response coefficient sets comprises convolving the symbol data with one-to-N-shifted decimated FIR aperture impulse response coefficient sets, wherein the one-to-N-shifted decimated FIR aperture impulse response coefficient sets are shifted by one-to-N samples with respect to the decimated FIR aperture impulse response coefficient set. 
     
     
       19. The filter of  claim 16 , wherein the FIR aperture impulse response coefficient set comprises a raised cosine FIR aperture impulse response or an impulse response modeled from Nyquist filtering functions. 
     
     
       20. The filter of  claim 16 , wherein the at least one processor is further configured to upsample symbol data at a sample per symbol rate of powers-of-two times three or powers-of-two.